Abstract
A model of a q-oscillator with quantum group symmetry H q (4) is put forward. The representations of the q-oscillator algebra H q (4) and solutions to the quantum q-oscillator system are provided. We find that the energy spectrum of the q-oscillator bears the essential properties of the observed spectra of diatomic molecules. When the parameters are determined phenomenologically, the spectrum of the q-oscillator coincides with the infrared, vibrational Raman spectra and vibrational structure of electronic transitions of the diatomic molecule.
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